Some beams of light of colour A and B mix and the result is new colour C. When we say colour, it means a spectrum that we perceive as that colour.
Some beams of light of spectrum A and spectrum B mix and the result is new spectrum C
Specturm C is spectrum A added to spectrum B, for each precise frequency range. The waves , or photons, do not join and change frequency to make the new colour C, they remain as they were in the original spectrum.
This allows spectrum analysis of stars.. Helium was first proposed as existing because its absorbtion lines were seen in the spectrum of the sun, the helium gas absobrbing that frequency, hence the name, the gas found in Helios - the sun. Other lines are brighter lines, the emmission from the hot gas. If the frequency changed to follow the percieved colour, by whatever mechansim, the lines seen as emission and absorbtion lines would be erased, the spectrum would just morph to be the new light at the frequency dictated by the resulting spectrum (ie, if its averaging to yellow in an optical sense of averaging, whatever that is, then all the waves becomes yellow waves ?) No.
Spectrums are preserved.
The photons cannot collide and neutralise each other. When the electrons jump energy levels, and have excess energy, they release a photon with that energy , by E=hf , right, There’s an energy conservation with these photons. Photons that would cancel if they were sound or water waves, well no, they, just pass through each other, conserving energy.